• Hagar GalEmail author
  • Fou-Lai Lin
  • Jia-Ming Ying


This study uses classroom videotapes to examine the phenomenon of students who are left behind during whole-class teaching. Zooming in via these videos enabled us to analyze these classroom situations by means of a compact, multi-perspective set of theories – van Hiele theory, conceptualization, and visual perception. The analysis provided a picture of the classroom interaction in which the sound of silence of those students who might not share understanding during the class discourse is ignored. Based on a sample of Taiwanese junior high school geometry classes, the study demonstrated how investigating situations of silence uncovered the possibility of teachers’ unawareness of student difficulties or their unsuccessful efforts to cope with them. Teachers’ post-lesson interviews and questionnaires shed additional light on the perspective of left-behind students. Implications of this method for pre- and in-service teachers’ programs are briefly discussed, and some recommendations for change are proposed.


class discourse geometry left behind low achievers problematic learning situations silence teachers’ awareness van Hiele theory 


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Supplementary material

10763_2008_9139_MOESM1_ESM.doc (5 kb)
ESM Table 1 Teachers’ background (DOC 31.0 KB)
10763_2008_9139_MOESM2_ESM.doc (32 kb)
ESM Table 2 Methods to detect Situations of Silence (SoS) and teachers’ perspectives (DOC 31.5 KB)
10763_2008_9139_MOESM3_ESM.doc (24 kb)
ESM Table 3 Relation of an angle at the circumference and the arc it contains (DOC 24.0 KB)
10763_2008_9139_MOESM4_ESM.doc (37 kb)
ESM Table 4 Relations between two circles (Episode 3a) (DOC 37.0 KB)
10763_2008_9139_MOESM5_ESM.doc (20 kb)
ESM 5 One of the most widely used and accepted methods in Taiwan’s elementary schools is the cooperative learning approach of the Student Teams Achievement Division (STAD), whose teaching process in Taiwan often includes a whole-class introduction, group practice, a quiz and group processing (e.g., Chang & Tsuei, 2006; Wang & Chang, 2003). There have also been some attempts to introduce cooperative approaches into high schools, with positive results (e.g., Chen & Yau, 2004). (DOC 19.5 KB)
10763_2008_9139_MOESM6_ESM.doc (20 kb)
ESM 6 International comparisons indicate that mathematics performance is remarkable in some countries, e.g., Singapore, Japan, Korea and Taiwan, as measured by TIMSS (Mullis, Martin, Gonzales, & Chrostowski 2004). However, a closer look reveals mixed results, suggesting that some students have been left behind. Though Taiwanese eighth graders achieved a high average score in TIMSS, 15% of them were situated below intermediate or low benchmarks. While this was much lower than the international average of 51%, Taiwan’s percentage was still higher than those of other “best achieving” countries (Singapore, South Korea, and Hong Kong). Moreover, the distribution of math achievements among all Taiwanese eighth graders is one of the widest (Mullis, Martin, Gonzales, & Chrostowski 2004). The initiative to address the problem and to improve achievements of the lower part of the scale invited enquiry of the left-behind phenomenon. (DOC 20.0 KB)


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Copyright information

© National Science Council, Taiwan 2008

Authors and Affiliations

  1. 1.David Yellin College of EducationJerusalemIsrael
  2. 2.National Taiwan Normal UniversityTaipeiTaiwan

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